Simplifying Polynomial Expressions worksheets - Free Printable
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Step-by-step solution for: Simplifying Polynomial Expressions worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Simplifying Polynomial Expressions worksheets
Let’s solve each problem step by step. We’re simplifying polynomial expressions — that means combining like terms (terms with the same power of x).
We’ll go one by one, carefully adding or subtracting coefficients for matching powers: x³, x², x, and constants.
---
1)
(16x³ + 7x² - 7x³) + (23x² - 23x³ + 14x²)
Group like terms:
x³: 16 - 7 - 23 = -14 → -14x³
x²: 7 + 23 + 14 = 44 → 44x²
No x or constant terms.
→ -14x³ + 44x²
---
2)
3x + 3x² + x³ + 3x - 3
Group:
x³: 1 → x³
x²: 3 → 3x²
x: 3 + 3 = 6 → 6x
constant: -3 → -3
→ x³ + 3x² + 6x - 3
---
3)
11x³ + 7x² - 5x³ + 16x² - 18x³ + 12x²
x³: 11 - 5 - 18 = -12 → -12x³
x²: 7 + 16 + 12 = 35 → 35x²
→ -12x³ + 35x²
---
4)
(10x³ + 5x² - 5x³) + (15x² - 15x³ + 10x²)
x³: 10 - 5 - 15 = -10 → -10x³
x²: 5 + 15 + 10 = 30 → 30x²
→ -10x³ + 30x²
---
5)
8x³ + 5x² - 2x³ + 10x² - 13x³ + 7x²
x³: 8 - 2 - 13 = -7 → -7x³
x²: 5 + 10 + 7 = 22 → 22x²
→ -7x³ + 22x²
---
6)
4x + 7x² - x³ + 5x
x³: -1 → -x³
x²: 7 → 7x²
x: 4 + 5 = 9 → 9x
→ -x³ + 7x² + 9x
---
7)
(13x³ + 4x² - 2x³) + (15x² - 17x³ + 6x²)
x³: 13 - 2 - 17 = -6 → -6x³
x²: 4 + 15 + 6 = 25 → 25x²
→ -6x³ + 25x²
---
8)
20x + 3x² + x³ + 4x - 4
x³: 1 → x³
x²: 3 → 3x²
x: 20 + 4 = 24 → 24x
constant: -4 → -4
→ x³ + 3x² + 24x - 4
---
9)
9x³ + 4x² - 5x³ + 14x² - 13x³ + 9x²
x³: 9 - 5 - 13 = -9 → -9x³
x²: 4 + 14 + 9 = 27 → 27x²
→ -9x³ + 27x²
---
10)
(7x³ + 6x² - 5x³) + (12x² - 13x³ + 11x²)
x³: 7 - 5 - 13 = -11 → -11x³
x²: 6 + 12 + 11 = 29 → 29x²
→ -11x³ + 29x²
---
11)
10x³ + 7x² - 2x³ + 12x² - 17x³ + 9x²
x³: 10 - 2 - 17 = -9 → -9x³
x²: 7 + 12 + 9 = 28 → 28x²
→ -9x³ + 28x²
---
12)
(6x³ + 7x² - 7x³) + (13x² - 13x³ + 14x²)
x³: 6 - 7 - 13 = -14 → -14x³
x²: 7 + 13 + 14 = 34 → 34x²
→ -14x³ + 34x²
---
13)
10x + 6x² - x³ + 7x
x³: -1 → -x³
x²: 6 → 6x²
x: 10 + 7 = 17 → 17x
→ -x³ + 6x² + 17x
---
14)
19x³ + 5x² - 4x³ + 23x² - 24x³ + 9x²
x³: 19 - 4 - 24 = -9 → -9x³
x²: 5 + 23 + 9 = 37 → 37x²
→ -9x³ + 37x²
---
15)
2x + 5x² + x³ + 3x - 3
x³: 1 → x³
x²: 5 → 5x²
x: 2 + 3 = 5 → 5x
constant: -3 → -3
→ x³ + 5x² + 5x - 3
---
16)
6x + 4x² + x³ + 7x - 7
x³: 1 → x³
x²: 4 → 4x²
x: 6 + 7 = 13 → 13x
constant: -7 → -7
→ x³ + 4x² + 13x - 7
---
17)
(11x³ + 6x² - 4x³) + (15x² - 17x³ + 10x²)
x³: 11 - 4 - 17 = -10 → -10x³
x²: 6 + 15 + 10 = 31 → 31x²
→ -10x³ + 31x²
---
18)
(5x³ + 5x² - 2x³) + (7x² - 10x³ + 7x²)
x³: 5 - 2 - 10 = -7 → -7x³
x²: 5 + 7 + 7 = 19 → 19x²
→ -7x³ + 19x²
---
19)
(14x³ + 7x² - 4x³) + (18x² - 21x³ + 11x²)
x³: 14 - 4 - 21 = -11 → -11x³
x²: 7 + 18 + 11 = 36 → 36x²
→ -11x³ + 36x²
---
20)
15x + 3x² - x³ + 4x
x³: -1 → -x³
x²: 3 → 3x²
x: 15 + 4 = 19 → 19x
→ -x³ + 3x² + 19x
---
21)
7x + 7x² - x³ + 7x
x³: -1 → -x³
x²: 7 → 7x²
x: 7 + 7 = 14 → 14x
→ -x³ + 7x² + 14x
---
22)
18x³ + 3x² - 4x³ + 22x² - 21x³ + 7x²
x³: 18 - 4 - 21 = -7 → -7x³
x²: 3 + 22 + 7 = 32 → 32x²
→ -7x³ + 32x²
---
23)
9x + 3x² - x³ + 7x
x³: -1 → -x³
x²: 3 → 3x²
x: 9 + 7 = 16 → 16x
→ -x³ + 3x² + 16x
---
24)
21x + 5x² - x³ + 3x
x³: -1 → -x³
x²: 5 → 5x²
x: 21 + 3 = 24 → 24x
→ -x³ + 5x² + 24x
---
25)
18x + 3x² + x³ + 3x - 3
x³: 1 → x³
x²: 3 → 3x²
x: 18 + 3 = 21 → 21x
constant: -3 → -3
→ x³ + 3x² + 21x - 3
---
26)
17x + 2x² - x³ + 5x
x³: -1 → -x³
x²: 2 → 2x²
x: 17 + 5 = 22 → 22x
→ -x³ + 2x² + 22x
---
27)
12x + 4x² + x³ + 3x - 3
x³: 1 → x³
x²: 4 → 4x²
x: 12 + 3 = 15 → 15x
constant: -3 → -3
→ x³ + 4x² + 15x - 3
---
28)
8x + 2x² - x³ + 5x
x³: -1 → -x³
x²: 2 → 2x²
x: 8 + 5 = 13 → 13x
→ -x³ + 2x² + 13x
---
29)
20x³ + 7x² - 3x³ + 23x² - 27x³ + 10x²
x³: 20 - 3 - 27 = -10 → -10x³
x²: 7 + 23 + 10 = 40 → 40x²
→ -10x³ + 40x²
---
30)
5x + 4x² + x³ + 4x - 4
x³: 1 → x³
x²: 4 → 4x²
x: 5 + 4 = 9 → 9x
constant: -4 → -4
→ x³ + 4x² + 9x - 4
---
Final Answer:
1) -14x³ + 44x²
2) x³ + 3x² + 6x - 3
3) -12x³ + 35x²
4) -10x³ + 30x²
5) -7x³ + 22x²
6) -x³ + 7x² + 9x
7) -6x³ + 25x²
8) x³ + 3x² + 24x - 4
9) -9x³ + 27x²
10) -11x³ + 29x²
11) -9x³ + 28x²
12) -14x³ + 34x²
13) -x³ + 6x² + 17x
14) -9x³ + 37x²
15) x³ + 5x² + 5x - 3
16) x³ + 4x² + 13x - 7
17) -10x³ + 31x²
18) -7x³ + 19x²
19) -11x³ + 36x²
20) -x³ + 3x² + 19x
21) -x³ + 7x² + 14x
22) -7x³ + 32x²
23) -x³ + 3x² + 16x
24) -x³ + 5x² + 24x
25) x³ + 3x² + 21x - 3
26) -x³ + 2x² + 22x
27) x³ + 4x² + 15x - 3
28) -x³ + 2x² + 13x
29) -10x³ + 40x²
30) x³ + 4x² + 9x - 4
We’ll go one by one, carefully adding or subtracting coefficients for matching powers: x³, x², x, and constants.
---
1)
(16x³ + 7x² - 7x³) + (23x² - 23x³ + 14x²)
Group like terms:
x³: 16 - 7 - 23 = -14 → -14x³
x²: 7 + 23 + 14 = 44 → 44x²
No x or constant terms.
→ -14x³ + 44x²
---
2)
3x + 3x² + x³ + 3x - 3
Group:
x³: 1 → x³
x²: 3 → 3x²
x: 3 + 3 = 6 → 6x
constant: -3 → -3
→ x³ + 3x² + 6x - 3
---
3)
11x³ + 7x² - 5x³ + 16x² - 18x³ + 12x²
x³: 11 - 5 - 18 = -12 → -12x³
x²: 7 + 16 + 12 = 35 → 35x²
→ -12x³ + 35x²
---
4)
(10x³ + 5x² - 5x³) + (15x² - 15x³ + 10x²)
x³: 10 - 5 - 15 = -10 → -10x³
x²: 5 + 15 + 10 = 30 → 30x²
→ -10x³ + 30x²
---
5)
8x³ + 5x² - 2x³ + 10x² - 13x³ + 7x²
x³: 8 - 2 - 13 = -7 → -7x³
x²: 5 + 10 + 7 = 22 → 22x²
→ -7x³ + 22x²
---
6)
4x + 7x² - x³ + 5x
x³: -1 → -x³
x²: 7 → 7x²
x: 4 + 5 = 9 → 9x
→ -x³ + 7x² + 9x
---
7)
(13x³ + 4x² - 2x³) + (15x² - 17x³ + 6x²)
x³: 13 - 2 - 17 = -6 → -6x³
x²: 4 + 15 + 6 = 25 → 25x²
→ -6x³ + 25x²
---
8)
20x + 3x² + x³ + 4x - 4
x³: 1 → x³
x²: 3 → 3x²
x: 20 + 4 = 24 → 24x
constant: -4 → -4
→ x³ + 3x² + 24x - 4
---
9)
9x³ + 4x² - 5x³ + 14x² - 13x³ + 9x²
x³: 9 - 5 - 13 = -9 → -9x³
x²: 4 + 14 + 9 = 27 → 27x²
→ -9x³ + 27x²
---
10)
(7x³ + 6x² - 5x³) + (12x² - 13x³ + 11x²)
x³: 7 - 5 - 13 = -11 → -11x³
x²: 6 + 12 + 11 = 29 → 29x²
→ -11x³ + 29x²
---
11)
10x³ + 7x² - 2x³ + 12x² - 17x³ + 9x²
x³: 10 - 2 - 17 = -9 → -9x³
x²: 7 + 12 + 9 = 28 → 28x²
→ -9x³ + 28x²
---
12)
(6x³ + 7x² - 7x³) + (13x² - 13x³ + 14x²)
x³: 6 - 7 - 13 = -14 → -14x³
x²: 7 + 13 + 14 = 34 → 34x²
→ -14x³ + 34x²
---
13)
10x + 6x² - x³ + 7x
x³: -1 → -x³
x²: 6 → 6x²
x: 10 + 7 = 17 → 17x
→ -x³ + 6x² + 17x
---
14)
19x³ + 5x² - 4x³ + 23x² - 24x³ + 9x²
x³: 19 - 4 - 24 = -9 → -9x³
x²: 5 + 23 + 9 = 37 → 37x²
→ -9x³ + 37x²
---
15)
2x + 5x² + x³ + 3x - 3
x³: 1 → x³
x²: 5 → 5x²
x: 2 + 3 = 5 → 5x
constant: -3 → -3
→ x³ + 5x² + 5x - 3
---
16)
6x + 4x² + x³ + 7x - 7
x³: 1 → x³
x²: 4 → 4x²
x: 6 + 7 = 13 → 13x
constant: -7 → -7
→ x³ + 4x² + 13x - 7
---
17)
(11x³ + 6x² - 4x³) + (15x² - 17x³ + 10x²)
x³: 11 - 4 - 17 = -10 → -10x³
x²: 6 + 15 + 10 = 31 → 31x²
→ -10x³ + 31x²
---
18)
(5x³ + 5x² - 2x³) + (7x² - 10x³ + 7x²)
x³: 5 - 2 - 10 = -7 → -7x³
x²: 5 + 7 + 7 = 19 → 19x²
→ -7x³ + 19x²
---
19)
(14x³ + 7x² - 4x³) + (18x² - 21x³ + 11x²)
x³: 14 - 4 - 21 = -11 → -11x³
x²: 7 + 18 + 11 = 36 → 36x²
→ -11x³ + 36x²
---
20)
15x + 3x² - x³ + 4x
x³: -1 → -x³
x²: 3 → 3x²
x: 15 + 4 = 19 → 19x
→ -x³ + 3x² + 19x
---
21)
7x + 7x² - x³ + 7x
x³: -1 → -x³
x²: 7 → 7x²
x: 7 + 7 = 14 → 14x
→ -x³ + 7x² + 14x
---
22)
18x³ + 3x² - 4x³ + 22x² - 21x³ + 7x²
x³: 18 - 4 - 21 = -7 → -7x³
x²: 3 + 22 + 7 = 32 → 32x²
→ -7x³ + 32x²
---
23)
9x + 3x² - x³ + 7x
x³: -1 → -x³
x²: 3 → 3x²
x: 9 + 7 = 16 → 16x
→ -x³ + 3x² + 16x
---
24)
21x + 5x² - x³ + 3x
x³: -1 → -x³
x²: 5 → 5x²
x: 21 + 3 = 24 → 24x
→ -x³ + 5x² + 24x
---
25)
18x + 3x² + x³ + 3x - 3
x³: 1 → x³
x²: 3 → 3x²
x: 18 + 3 = 21 → 21x
constant: -3 → -3
→ x³ + 3x² + 21x - 3
---
26)
17x + 2x² - x³ + 5x
x³: -1 → -x³
x²: 2 → 2x²
x: 17 + 5 = 22 → 22x
→ -x³ + 2x² + 22x
---
27)
12x + 4x² + x³ + 3x - 3
x³: 1 → x³
x²: 4 → 4x²
x: 12 + 3 = 15 → 15x
constant: -3 → -3
→ x³ + 4x² + 15x - 3
---
28)
8x + 2x² - x³ + 5x
x³: -1 → -x³
x²: 2 → 2x²
x: 8 + 5 = 13 → 13x
→ -x³ + 2x² + 13x
---
29)
20x³ + 7x² - 3x³ + 23x² - 27x³ + 10x²
x³: 20 - 3 - 27 = -10 → -10x³
x²: 7 + 23 + 10 = 40 → 40x²
→ -10x³ + 40x²
---
30)
5x + 4x² + x³ + 4x - 4
x³: 1 → x³
x²: 4 → 4x²
x: 5 + 4 = 9 → 9x
constant: -4 → -4
→ x³ + 4x² + 9x - 4
---
Final Answer:
1) -14x³ + 44x²
2) x³ + 3x² + 6x - 3
3) -12x³ + 35x²
4) -10x³ + 30x²
5) -7x³ + 22x²
6) -x³ + 7x² + 9x
7) -6x³ + 25x²
8) x³ + 3x² + 24x - 4
9) -9x³ + 27x²
10) -11x³ + 29x²
11) -9x³ + 28x²
12) -14x³ + 34x²
13) -x³ + 6x² + 17x
14) -9x³ + 37x²
15) x³ + 5x² + 5x - 3
16) x³ + 4x² + 13x - 7
17) -10x³ + 31x²
18) -7x³ + 19x²
19) -11x³ + 36x²
20) -x³ + 3x² + 19x
21) -x³ + 7x² + 14x
22) -7x³ + 32x²
23) -x³ + 3x² + 16x
24) -x³ + 5x² + 24x
25) x³ + 3x² + 21x - 3
26) -x³ + 2x² + 22x
27) x³ + 4x² + 15x - 3
28) -x³ + 2x² + 13x
29) -10x³ + 40x²
30) x³ + 4x² + 9x - 4
Parent Tip: Review the logic above to help your child master the concept of simplifying polynomials worksheet.
